Zulip Chat Archive
Stream: new members
Topic: What does two dots mean in front of an identifier
Lars Ericson (Dec 09 2020 at 18:07):
What does the last line of this mean, in particular the ..
in ..induced_outer_measure
:
def of_measurable {α} [measurable_space α]
(m : Π (s : set α), is_measurable s → ennreal)
(m0 : m ∅ is_measurable.empty = 0)
(mU : ∀ {{f : ℕ → set α}} (h : ∀i, is_measurable (f i)),
pairwise (disjoint on f) →
m (⋃i, f i) (is_measurable.Union h) = (∑'i, m (f i) (h i))) :
measure α :=
{ m_Union := λ f hf hd,
show induced_outer_measure m _ m0 (Union f) =
∑' i, induced_outer_measure m _ m0 (f i), begin
rw [induced_outer_measure_eq m0 mU, mU hf hd],
congr, funext n, rw induced_outer_measure_eq m0 mU
end,
trimmed :=
show (induced_outer_measure m _ m0).trim = induced_outer_measure m _ m0, begin
unfold outer_measure.trim,
congr, funext s hs,
exact induced_outer_measure_eq m0 mU hs
end,
..induced_outer_measure m _ m0 }
Eric Wieser (Dec 09 2020 at 18:15):
Unpack the fields of the structure to the right of the dots into the containing structure
Bryan Gin-ge Chen (Dec 09 2020 at 18:18):
This is called the "record update syntax" in 9.2 of TPiL.
Last updated: Dec 20 2023 at 11:08 UTC